LMFDB - Embedded newform 1900.2.l.b.1557.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(493,1900)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1900.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} + \cdots + 1370 $ x^12 - 4x^11 + 28x^10 - 64x^9 + 236x^8 - 420x^7 + 946x^6 - 1216x^5 + 1896x^4 - 1564x^3 + 2284x^2 - 1088*x + 1370
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1557.6
Root			$1.24060 - 3.49408i$ of defining polynomial
Character	$\chi$	$=$	1900.1557
Dual form			1900.2.l.b.493.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25348 + 2.25348i) q^{3} +(1.48119 + 1.48119i) q^{7} +7.15633i q^{9} +O(q^{10})$	$q+(2.25348 + 2.25348i) q^{3} +(1.48119 + 1.48119i) q^{7} +7.15633i q^{9} +0.806063 q^{11} +(-0.437032 - 0.437032i) q^{13} +(-3.15633 - 3.15633i) q^{17} +(-1.81645 + 3.96239i) q^{19} +6.67568i q^{21} +(-1.86907 + 1.86907i) q^{23} +(-9.36619 + 9.36619i) q^{27} +4.50696 q^{29} +6.67568i q^{31} +(1.81645 + 1.81645i) q^{33} +(5.29626 - 5.29626i) q^{37} -1.96968i q^{39} +11.1826i q^{41} +(3.86907 - 3.86907i) q^{43} +(-6.83146 - 6.83146i) q^{47} -2.61213i q^{49} -14.2254i q^{51} +(8.92916 + 8.92916i) q^{53} +(-13.0225 + 4.83583i) q^{57} -12.9308 q^{59} -2.15633 q^{61} +(-10.5999 + 10.5999i) q^{63} +(4.94399 - 4.94399i) q^{67} -8.42380 q^{69} -3.04278i q^{71} +(6.19394 - 6.19394i) q^{73} +(1.19394 + 1.19394i) q^{77} +1.46417 q^{79} -20.7440 q^{81} +(-5.32487 + 5.32487i) q^{83} +(10.1563 + 10.1563i) q^{87} +14.2254 q^{89} -1.29466i q^{91} +(-15.0435 + 15.0435i) q^{93} +(7.46498 - 7.46498i) q^{97} +5.76845i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{7}+O(q^{10}) $ 12 * q - 4 * q^7	$ 12 q - 4 q^{7} + 8 q^{11} + 4 q^{17} - 4 q^{23} + 28 q^{43} - 20 q^{47} - 24 q^{57} + 16 q^{61} - 20 q^{63} + 76 q^{73} + 16 q^{77} + 4 q^{81} - 84 q^{83} + 80 q^{87} - 8 q^{93}+O(q^{100}) $ 12 * q - 4 * q^7 + 8 * q^11 + 4 * q^17 - 4 * q^23 + 28 * q^43 - 20 * q^47 - 24 * q^57 + 16 * q^61 - 20 * q^63 + 76 * q^73 + 16 * q^77 + 4 * q^81 - 84 * q^83 + 80 * q^87 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.25348	+	2.25348i	1.30105	+	1.30105i	0.927687	+	0.373359i	$0.121794\pi$
$3$	2.25348	+	2.25348i	1.30105	+	1.30105i	0.373359	+	0.927687i	$0.378206\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.48119	+	1.48119i	0.559839	+	0.559839i	0.929261	−	0.369423i	$-0.120445\pi$
$7$	1.48119	+	1.48119i	0.559839	+	0.559839i	−0.369423	+	0.929261i	$0.620445\pi$
$8$		0			0
$9$			7.15633i			2.38544i
$10$		0			0
$11$	0.806063			0.243037			0.121519	−	0.992589i	$-0.461224\pi$
$11$	0.806063			0.243037			0.121519	+	0.992589i	$0.461224\pi$
$12$		0			0
$13$	−0.437032	−	0.437032i	−0.121211	−	0.121211i	0.643899	−	0.765110i	$-0.277316\pi$
$13$	−0.437032	−	0.437032i	−0.121211	−	0.121211i	−0.765110	+	0.643899i	$0.777316\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.15633	−	3.15633i	−0.765521	−	0.765521i	0.211793	−	0.977315i	$-0.432070\pi$
$17$	−3.15633	−	3.15633i	−0.765521	−	0.765521i	−0.977315	+	0.211793i	$0.932070\pi$
$18$		0			0
$19$	−1.81645	+	3.96239i	−0.416721	+	0.909034i
$19$	−1.81645	+	3.96239i	−0.416721	+	0.909034i
$20$		0			0
$21$			6.67568i			1.45675i
$22$		0			0
$23$	−1.86907	+	1.86907i	−0.389728	+	0.389728i	−0.874590	−	0.484863i	$-0.838870\pi$
$23$	−1.86907	+	1.86907i	−0.389728	+	0.389728i	0.484863	+	0.874590i	$0.338870\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−9.36619	+	9.36619i	−1.80252	+	1.80252i
$28$		0			0
$29$	4.50696			0.836921			0.418460	−	0.908235i	$-0.362570\pi$
$29$	4.50696			0.836921			0.418460	+	0.908235i	$0.362570\pi$
$30$		0			0
$31$			6.67568i			1.19899i	0.800380	+	0.599494i	$0.204631\pi$
$31$			6.67568i			1.19899i	−0.800380	+	0.599494i	$0.795369\pi$
$32$		0			0
$33$	1.81645	+	1.81645i	0.316203	+	0.316203i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.29626	−	5.29626i	0.870700	−	0.870700i	−0.121848	−	0.992549i	$-0.538882\pi$
$37$	5.29626	−	5.29626i	0.870700	−	0.870700i	0.992549	+	0.121848i	$0.0388822\pi$
$38$		0			0
$39$		−	1.96968i		−	0.315402i
$40$		0			0
$41$			11.1826i			1.74643i	0.487332	+	0.873217i	$0.337970\pi$
$41$			11.1826i			1.74643i	−0.487332	+	0.873217i	$0.662030\pi$
$42$		0			0
$43$	3.86907	−	3.86907i	0.590027	−	0.590027i	−0.347611	−	0.937639i	$-0.613007\pi$
$43$	3.86907	−	3.86907i	0.590027	−	0.590027i	0.937639	+	0.347611i	$0.113007\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.83146	−	6.83146i	−0.996470	−	0.996470i	0.00352351	−	0.999994i	$-0.498878\pi$
$47$	−6.83146	−	6.83146i	−0.996470	−	0.996470i	−0.999994	+	0.00352351i	$0.998878\pi$
$48$		0			0
$49$		−	2.61213i		−	0.373161i
$50$		0			0
$51$		−	14.2254i		−	1.99196i
$52$		0			0
$53$	8.92916	+	8.92916i	1.22651	+	1.22651i	0.965274	+	0.261240i	$0.0841314\pi$
$53$	8.92916	+	8.92916i	1.22651	+	1.22651i	0.261240	+	0.965274i	$0.415869\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−13.0225	+	4.83583i	−1.72487	+	0.640522i
$58$		0			0
$59$	−12.9308			−1.68344			−0.841721	−	0.539913i	$-0.818457\pi$
$59$	−12.9308			−1.68344			−0.841721	+	0.539913i	$0.818457\pi$
$60$		0			0
$61$	−2.15633			−0.276089			−0.138045	−	0.990426i	$-0.544082\pi$
$61$	−2.15633			−0.276089			−0.138045	+	0.990426i	$0.544082\pi$
$62$		0			0
$63$	−10.5999	+	10.5999i	−1.33546	+	1.33546i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.94399	−	4.94399i	0.604004	−	0.604004i	−0.337368	−	0.941373i	$-0.609537\pi$
$67$	4.94399	−	4.94399i	0.604004	−	0.604004i	0.941373	+	0.337368i	$0.109537\pi$
$68$		0			0
$69$	−8.42380			−1.01411
$70$		0			0
$71$		−	3.04278i		−	0.361112i	−0.983565	−	0.180556i	$-0.942210\pi$
$71$		−	3.04278i		−	0.361112i	0.983565	−	0.180556i	$-0.0577897\pi$
$72$		0			0
$73$	6.19394	−	6.19394i	0.724945	−	0.724945i	−0.244663	−	0.969608i	$-0.578677\pi$
$73$	6.19394	−	6.19394i	0.724945	−	0.724945i	0.969608	+	0.244663i	$0.0786773\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.19394	+	1.19394i	0.136062	+	0.136062i
$78$		0			0
$79$	1.46417			0.164732			0.0823660	−	0.996602i	$-0.473752\pi$
$79$	1.46417			0.164732			0.0823660	+	0.996602i	$0.473752\pi$
$80$		0			0
$81$	−20.7440			−2.30489
$82$		0			0
$83$	−5.32487	+	5.32487i	−0.584480	+	0.584480i	−0.936131	−	0.351651i	$-0.885620\pi$
$83$	−5.32487	+	5.32487i	−0.584480	+	0.584480i	0.351651	+	0.936131i	$0.385620\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	10.1563	+	10.1563i	1.08887	+	1.08887i
$88$		0			0
$89$	14.2254			1.50789			0.753946	−	0.656937i	$-0.228148\pi$
$89$	14.2254			1.50789			0.753946	+	0.656937i	$0.228148\pi$
$90$		0			0
$91$		−	1.29466i		−	0.135717i
$92$		0			0
$93$	−15.0435	+	15.0435i	−1.55994	+	1.55994i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.46498	−	7.46498i	0.757954	−	0.757954i	−0.217995	−	0.975950i	$-0.569952\pi$
$97$	7.46498	−	7.46498i	0.757954	−	0.757954i	0.975950	+	0.217995i	$0.0699518\pi$
$98$		0			0
$99$			5.76845i			0.579751i
$100$		0			0
$101$	4.08110			0.406085			0.203042	−	0.979170i	$-0.434917\pi$
$101$	4.08110			0.406085			0.203042	+	0.979170i	$0.434917\pi$
$102$		0			0
$103$	−1.31110	−	1.31110i	−0.129186	−	0.129186i	0.639557	−	0.768743i	$-0.279118\pi$
$103$	−1.31110	−	1.31110i	−0.129186	−	0.129186i	−0.768743	+	0.639557i	$0.779118\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.11271	−	7.11271i	0.687612	−	0.687612i	−0.274092	−	0.961703i	$-0.588377\pi$
$107$	7.11271	−	7.11271i	0.687612	−	0.687612i	0.961703	+	0.274092i	$0.0883773\pi$
$108$		0			0
$109$	19.3225			1.85076			0.925379	−	0.379043i	$-0.123747\pi$
$109$	19.3225			1.85076			0.925379	+	0.379043i	$0.123747\pi$
$110$		0			0
$111$	23.8700			2.26564
$112$		0			0
$113$	−6.23865	−	6.23865i	−0.586882	−	0.586882i	0.349903	−	0.936786i	$-0.386214\pi$
$113$	−6.23865	−	6.23865i	−0.586882	−	0.586882i	−0.936786	+	0.349903i	$0.886214\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.12754	−	3.12754i	0.289141	−	0.289141i
$118$		0			0
$119$		−	9.35026i		−	0.857137i
$120$		0			0
$121$	−10.3503			−0.940933
$122$		0			0
$123$	−25.1998	+	25.1998i	−2.27219	+	2.27219i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.80322	+	9.80322i	−0.869895	+	0.869895i	−0.992460	−	0.122565i	$-0.960888\pi$
$127$	−9.80322	+	9.80322i	−0.869895	+	0.869895i	0.122565	+	0.992460i	$0.460888\pi$
$128$		0			0
$129$	17.4377			1.53531
$130$		0			0
$131$	−9.14903			−0.799355			−0.399677	−	0.916656i	$-0.630878\pi$
$131$	−9.14903			−0.799355			−0.399677	+	0.916656i	$0.630878\pi$
$132$		0			0
$133$	−8.55958	+	3.17856i	−0.742209	+	0.275616i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.18664	−	3.18664i	−0.272253	−	0.272253i	0.557753	−	0.830007i	$-0.311663\pi$
$137$	−3.18664	−	3.18664i	−0.272253	−	0.272253i	−0.830007	+	0.557753i	$0.811663\pi$
$138$		0			0
$139$			15.2447i			1.29304i	0.762897	+	0.646520i	$0.223776\pi$
$139$			15.2447i			1.29304i	−0.762897	+	0.646520i	$0.776224\pi$
$140$		0			0
$141$		−	30.7891i		−	2.59291i
$142$		0			0
$143$	−0.352275	−	0.352275i	−0.0294587	−	0.0294587i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.88637	−	5.88637i	0.485500	−	0.485500i
$148$		0			0
$149$		−	15.3806i		−	1.26003i	−0.776585	−	0.630013i	$-0.783050\pi$
$149$		−	15.3806i		−	1.26003i	0.776585	−	0.630013i	$-0.216950\pi$
$150$		0			0
$151$			5.21151i			0.424106i	0.977258	+	0.212053i	$0.0680150\pi$
$151$			5.21151i			0.424106i	−0.977258	+	0.212053i	$0.931985\pi$
$152$		0			0
$153$	22.5877	−	22.5877i	1.82611	−	1.82611i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	10.2447	+	10.2447i	0.817618	+	0.817618i	0.985762	−	0.168145i	$-0.0537775\pi$
$157$	10.2447	+	10.2447i	0.817618	+	0.817618i	−0.168145	+	0.985762i	$0.553778\pi$
$158$		0			0
$159$			40.2433i			3.19150i
$160$		0			0
$161$	−5.53690			−0.436369
$162$		0			0
$163$	10.4133	−	10.4133i	0.815630	−	0.815630i	−0.169841	−	0.985471i	$-0.554326\pi$
$163$	10.4133	−	10.4133i	0.815630	−	0.815630i	0.985471	+	0.169841i	$0.0543256\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.42220	+	4.42220i	−0.342200	+	0.342200i	−0.857194	−	0.514994i	$-0.827794\pi$
$167$	−4.42220	+	4.42220i	−0.342200	+	0.342200i	0.514994	+	0.857194i	$0.327794\pi$
$168$		0			0
$169$		−	12.6180i		−	0.970616i
$170$		0			0
$171$	−28.3561	−	12.9991i	−2.16845	−	0.994064i
$172$		0			0
$173$	−4.06992	−	4.06992i	−0.309431	−	0.309431i	0.535258	−	0.844689i	$-0.320214\pi$
$173$	−4.06992	−	4.06992i	−0.309431	−	0.309431i	−0.844689	+	0.535258i	$0.820214\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−29.1392	−	29.1392i	−2.19024	−	2.19024i
$178$		0			0
$179$	2.87327			0.214758			0.107379	−	0.994218i	$-0.465754\pi$
$179$	2.87327			0.214758			0.107379	+	0.994218i	$0.465754\pi$
$180$		0			0
$181$			18.0278i			1.34000i	0.742362	+	0.669999i	$0.233705\pi$
$181$			18.0278i			1.34000i	−0.742362	+	0.669999i	$0.766295\pi$
$182$		0			0
$183$	−4.85923	−	4.85923i	−0.359205	−	0.359205i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.54420	−	2.54420i	−0.186050	−	0.186050i
$188$		0			0
$189$	−27.7463			−2.01825
$190$		0			0
$191$	−4.43866			−0.321170			−0.160585	−	0.987022i	$-0.551338\pi$
$191$	−4.43866			−0.321170			−0.160585	+	0.987022i	$0.551338\pi$
$192$		0			0
$193$	−4.42220	−	4.42220i	−0.318317	−	0.318317i	0.529804	−	0.848120i	$-0.322266\pi$
$193$	−4.42220	−	4.42220i	−0.318317	−	0.318317i	−0.848120	+	0.529804i	$0.822266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.3806	−	10.3806i	−0.739586	−	0.739586i	0.232912	−	0.972498i	$-0.425175\pi$
$197$	−10.3806	−	10.3806i	−0.739586	−	0.739586i	−0.972498	+	0.232912i	$0.925175\pi$
$198$		0			0
$199$		−	8.23743i		−	0.583936i	−0.956428	−	0.291968i	$-0.905690\pi$
$199$		−	8.23743i		−	0.583936i	0.956428	−	0.291968i	$-0.0943100\pi$
$200$		0			0
$201$	22.2823			1.57167
$202$		0			0
$203$	6.67568	+	6.67568i	0.468541	+	0.468541i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−13.3757	−	13.3757i	−0.929672	−	0.929672i
$208$		0			0
$209$	−1.46417	+	3.19394i	−0.101279	+	0.220929i
$210$		0			0
$211$		−	22.5348i		−	1.55136i	−0.631128	−	0.775679i	$-0.717408\pi$
$211$		−	22.5348i		−	1.55136i	0.631128	−	0.775679i	$-0.282592\pi$
$212$		0			0
$213$	6.85685	−	6.85685i	0.469824	−	0.469824i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−9.88798	+	9.88798i	−0.671239	+	0.671239i
$218$		0			0
$219$	27.9158			1.88637
$220$		0			0
$221$			2.75883i			0.185579i
$222$		0			0
$223$	13.4361	+	13.4361i	0.899749	+	0.899749i	0.995414	−	0.0956650i	$-0.0304978\pi$
$223$	13.4361	+	13.4361i	0.899749	+	0.899749i	−0.0956650	+	0.995414i	$0.530498\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.06992	+	4.06992i	−0.270130	+	0.270130i	−0.829153	−	0.559022i	$-0.811177\pi$
$227$	−4.06992	+	4.06992i	−0.270130	+	0.270130i	0.559022	+	0.829153i	$0.311177\pi$
$228$		0			0
$229$			4.46898i			0.295318i	0.989038	+	0.147659i	$0.0471738\pi$
$229$			4.46898i			0.295318i	−0.989038	+	0.147659i	$0.952826\pi$
$230$		0			0
$231$			5.38102i			0.354045i
$232$		0			0
$233$	11.1114	−	11.1114i	0.727933	−	0.727933i	−0.242274	−	0.970208i	$-0.577893\pi$
$233$	11.1114	−	11.1114i	0.727933	−	0.727933i	0.970208	+	0.242274i	$0.0778934\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.29948	+	3.29948i	0.214324	+	0.214324i
$238$		0			0
$239$		−	10.4387i		−	0.675221i	−0.941286	−	0.337610i	$-0.890381\pi$
$239$		−	10.4387i		−	0.675221i	0.941286	−	0.337610i	$-0.109619\pi$
$240$		0			0
$241$			13.6353i			0.878328i	0.898407	+	0.439164i	$0.144725\pi$
$241$			13.6353i			0.878328i	−0.898407	+	0.439164i	$0.855275\pi$
$242$		0			0
$243$	−18.6476	−	18.6476i	−1.19625	−	1.19625i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.52553	−	0.937845i	0.160696	−	0.0596737i
$248$		0			0
$249$	−23.9989			−1.52087
$250$		0			0
$251$	8.96239			0.565701			0.282850	−	0.959164i	$-0.408720\pi$
$251$	8.96239			0.565701			0.282850	+	0.959164i	$0.408720\pi$
$252$		0			0
$253$	−1.50659	+	1.50659i	−0.0947183	+	0.0947183i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.76043	−	6.76043i	0.421704	−	0.421704i	−0.464086	−	0.885790i	$-0.653617\pi$
$257$	6.76043	−	6.76043i	0.421704	−	0.421704i	0.885790	+	0.464086i	$0.153617\pi$
$258$		0			0
$259$	15.6896			0.974904
$260$		0			0
$261$			32.2532i			1.99643i
$262$		0			0
$263$	4.36248	−	4.36248i	0.269002	−	0.269002i	−0.559696	−	0.828698i	$-0.689082\pi$
$263$	4.36248	−	4.36248i	0.269002	−	0.269002i	0.828698	+	0.559696i	$0.189082\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	32.0567	+	32.0567i	1.96184	+	1.96184i
$268$		0			0
$269$	17.4377			1.06320			0.531598	−	0.846997i	$-0.321592\pi$
$269$	17.4377			1.06320			0.531598	+	0.846997i	$0.321592\pi$
$270$		0			0
$271$	−8.28233			−0.503116			−0.251558	−	0.967842i	$-0.580943\pi$
$271$	−8.28233			−0.503116			−0.251558	+	0.967842i	$0.580943\pi$
$272$		0			0
$273$	2.91748	−	2.91748i	0.176574	−	0.176574i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.80606	+	9.80606i	0.589189	+	0.589189i	0.937412	−	0.348223i	$-0.113215\pi$
$277$	9.80606	+	9.80606i	0.589189	+	0.589189i	−0.348223	+	0.937412i	$0.613215\pi$
$278$		0			0
$279$	−47.7733			−2.86011
$280$		0			0
$281$		−	5.66498i		−	0.337944i	−0.985621	−	0.168972i	$-0.945955\pi$
$281$		−	5.66498i		−	0.337944i	0.985621	−	0.168972i	$-0.0540448\pi$
$282$		0			0
$283$	−4.18172	+	4.18172i	−0.248577	+	0.248577i	−0.820387	−	0.571809i	$-0.806242\pi$
$283$	−4.18172	+	4.18172i	−0.248577	+	0.248577i	0.571809	+	0.820387i	$0.306242\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−16.5637	+	16.5637i	−0.977721	+	0.977721i
$288$		0			0
$289$			2.92478i			0.172046i
$290$		0			0
$291$	33.6444			1.97227
$292$		0			0
$293$	−7.35054	−	7.35054i	−0.429423	−	0.429423i	0.459009	−	0.888432i	$-0.348205\pi$
$293$	−7.35054	−	7.35054i	−0.429423	−	0.429423i	−0.888432	+	0.459009i	$0.848205\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−7.54974	+	7.54974i	−0.438080	+	0.438080i
$298$		0			0
$299$	1.63368			0.0944784
$300$		0			0
$301$	11.4617			0.660640
$302$		0			0
$303$	9.19667	+	9.19667i	0.528335	+	0.528335i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	23.3924	−	23.3924i	1.33508	−	1.33508i	0.434313	−	0.900762i	$-0.356991\pi$
$307$	23.3924	−	23.3924i	1.33508	−	1.33508i	0.900762	−	0.434313i	$-0.143009\pi$
$308$		0			0
$309$		−	5.90905i		−	0.336154i
$310$		0			0
$311$	11.2546			0.638188			0.319094	−	0.947723i	$-0.396621\pi$
$311$	11.2546			0.638188			0.319094	+	0.947723i	$0.396621\pi$
$312$		0			0
$313$	−14.5369	+	14.5369i	−0.821674	+	0.821674i	−0.986348	−	0.164674i	$-0.947343\pi$
$313$	−14.5369	+	14.5369i	−0.821674	+	0.821674i	0.164674	+	0.986348i	$0.447343\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.87154	+	9.87154i	−0.554441	+	0.554441i	−0.927719	−	0.373279i	$-0.878234\pi$
$317$	−9.87154	+	9.87154i	−0.554441	+	0.554441i	0.373279	+	0.927719i	$0.378234\pi$
$318$		0			0
$319$	3.63289			0.203403
$320$		0			0
$321$	32.0567			1.78923
$322$		0			0
$323$	18.2399	−	6.77329i	1.01489	−	0.376876i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	43.5428	+	43.5428i	2.40792	+	2.40792i
$328$		0			0
$329$		−	20.2374i		−	1.11573i
$330$		0			0
$331$			20.3110i			1.11639i	0.829709	+	0.558196i	$0.188506\pi$
$331$			20.3110i			1.11639i	−0.829709	+	0.558196i	$0.811494\pi$
$332$		0			0
$333$	37.9018	+	37.9018i	2.07700	+	2.07700i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	11.7892	−	11.7892i	0.642197	−	0.642197i	−0.308898	−	0.951095i	$-0.599960\pi$
$337$	11.7892	−	11.7892i	0.642197	−	0.642197i	0.951095	+	0.308898i	$0.0999601\pi$
$338$		0			0
$339$		−	28.1173i		−	1.52712i
$340$		0			0
$341$			5.38102i			0.291399i
$342$		0			0
$343$	14.2374	−	14.2374i	0.768749	−	0.768749i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−18.6302	−	18.6302i	−1.00012	−	1.00012i	−1.00000		0.000122901i	$-0.999961\pi$
$347$	−18.6302	−	18.6302i	−1.00012	−	1.00012i	−0.000122901	−	1.00000i	$-0.500039\pi$
$348$		0			0
$349$		−	21.0640i		−	1.12753i	−0.825936	−	0.563764i	$-0.809353\pi$
$349$		−	21.0640i		−	1.12753i	0.825936	−	0.563764i	$-0.190647\pi$
$350$		0			0
$351$	8.18664			0.436971
$352$		0			0
$353$	1.99271	−	1.99271i	0.106061	−	0.106061i	−0.652085	−	0.758146i	$-0.726105\pi$
$353$	1.99271	−	1.99271i	0.106061	−	0.106061i	0.758146	+	0.652085i	$0.226105\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	21.0706	−	21.0706i	1.11517	−	1.11517i
$358$		0			0
$359$			28.6458i			1.51187i	0.654649	+	0.755933i	$0.272816\pi$
$359$			28.6458i			1.51187i	−0.654649	+	0.755933i	$0.727184\pi$
$360$		0			0
$361$	−12.4010	−	14.3949i	−0.652687	−	0.757628i
$362$		0			0
$363$	−23.3241	−	23.3241i	−1.22420	−	1.22420i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.1368	+	12.1368i	0.633536	+	0.633536i	0.948953	−	0.315417i	$-0.102144\pi$
$367$	12.1368	+	12.1368i	0.633536	+	0.633536i	−0.315417	+	0.948953i	$0.602144\pi$
$368$		0			0
$369$	−80.0266			−4.16602
$370$		0			0
$371$			26.4516i			1.37330i
$372$		0			0
$373$	16.4789	+	16.4789i	0.853245	+	0.853245i	0.990531	−	0.137286i	$-0.0438381\pi$
$373$	16.4789	+	16.4789i	0.853245	+	0.853245i	−0.137286	+	0.990531i	$0.543838\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.96968	−	1.96968i	−0.101444	−	0.101444i
$378$		0			0
$379$	−2.92834			−0.150419			−0.0752094	−	0.997168i	$-0.523963\pi$
$379$	−2.92834			−0.150419			−0.0752094	+	0.997168i	$0.523963\pi$
$380$		0			0
$381$	−44.1827			−2.26355
$382$		0			0
$383$	21.3381	+	21.3381i	1.09033	+	1.09033i	0.995493	+	0.0948343i	$0.0302321\pi$
$383$	21.3381	+	21.3381i	1.09033	+	1.09033i	0.0948343	+	0.995493i	$0.469768\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	27.6883	+	27.6883i	1.40748	+	1.40748i
$388$		0			0
$389$			24.5647i			1.24548i	0.782430	+	0.622739i	$0.213980\pi$
$389$			24.5647i			1.24548i	−0.782430	+	0.622739i	$0.786020\pi$
$390$		0			0
$391$	11.7988			0.596689
$392$		0			0
$393$	−20.6171	−	20.6171i	−1.04000	−	1.04000i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.23155	+	5.23155i	0.262564	+	0.262564i	0.826095	−	0.563531i	$-0.190557\pi$
$397$	5.23155	+	5.23155i	0.262564	+	0.262564i	−0.563531	+	0.826095i	$0.690557\pi$
$398$		0			0
$399$	−26.4516	−	12.1260i	−1.32424	−	0.607060i
$400$		0			0
$401$		−	18.7324i		−	0.935450i	−0.883874	−	0.467725i	$-0.845074\pi$
$401$		−	18.7324i		−	0.935450i	0.883874	−	0.467725i	$-0.154926\pi$
$402$		0			0
$403$	2.91748	−	2.91748i	0.145330	−	0.145330i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.26912	−	4.26912i	0.211613	−	0.211613i
$408$		0			0
$409$	14.9850			0.740962			0.370481	−	0.928840i	$-0.379193\pi$
$409$	14.9850			0.740962			0.370481	+	0.928840i	$0.379193\pi$
$410$		0			0
$411$		−	14.3621i		−	0.708428i
$412$		0			0
$413$	−19.1530	−	19.1530i	−0.942456	−	0.942456i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−34.3536	+	34.3536i	−1.68231	+	1.68231i
$418$		0			0
$419$		−	34.2882i		−	1.67509i	−0.546369	−	0.837544i	$-0.683990\pi$
$419$		−	34.2882i		−	1.67509i	0.546369	−	0.837544i	$-0.316010\pi$
$420$		0			0
$421$		−	21.6056i		−	1.05299i	−0.850177	−	0.526497i	$-0.823505\pi$
$421$		−	21.6056i		−	1.05299i	0.850177	−	0.526497i	$-0.176495\pi$
$422$		0			0
$423$	48.8881	−	48.8881i	2.37702	−	2.37702i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.19394	−	3.19394i	−0.154565	−	0.154565i
$428$		0			0
$429$		−	1.58769i		−	0.0766544i
$430$		0			0
$431$			19.7431i			0.950990i	0.879718	+	0.475495i	$0.157731\pi$
$431$			19.7431i			0.950990i	−0.879718	+	0.475495i	$0.842269\pi$
$432$		0			0
$433$	11.0296	+	11.0296i	0.530047	+	0.530047i	0.920586	−	0.390539i	$-0.127712\pi$
$433$	11.0296	+	11.0296i	0.530047	+	0.530047i	−0.390539	+	0.920586i	$0.627712\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.01091	−	10.8010i	−0.191868	−	0.516683i
$438$		0			0
$439$	−12.3628			−0.590047			−0.295023	−	0.955490i	$-0.595327\pi$
$439$	−12.3628			−0.590047			−0.295023	+	0.955490i	$0.595327\pi$
$440$		0			0
$441$	18.6932			0.890154
$442$		0			0
$443$	−11.1744	+	11.1744i	−0.530913	+	0.530913i	−0.920844	−	0.389931i	$-0.872499\pi$
$443$	−11.1744	+	11.1744i	−0.530913	+	0.530913i	0.389931	+	0.920844i	$0.372499\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	34.6598	−	34.6598i	1.63935	−	1.63935i
$448$		0			0
$449$	2.90615			0.137150			0.0685748	−	0.997646i	$-0.478155\pi$
$449$	2.90615			0.137150			0.0685748	+	0.997646i	$0.478155\pi$
$450$		0			0
$451$			9.01391i			0.424449i
$452$		0			0
$453$	−11.7440	+	11.7440i	−0.551782	+	0.551782i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.1490	−	14.1490i	−0.661864	−	0.661864i	0.293955	−	0.955819i	$-0.405028\pi$
$457$	−14.1490	−	14.1490i	−0.661864	−	0.661864i	−0.955819	+	0.293955i	$0.905028\pi$
$458$		0			0
$459$	59.1255			2.75974
$460$		0			0
$461$	−18.6859			−0.870291			−0.435145	−	0.900360i	$-0.643303\pi$
$461$	−18.6859			−0.870291			−0.435145	+	0.900360i	$0.643303\pi$
$462$		0			0
$463$	−0.906679	+	0.906679i	−0.0421369	+	0.0421369i	−0.727861	−	0.685724i	$-0.759486\pi$
$463$	−0.906679	+	0.906679i	−0.0421369	+	0.0421369i	0.685724	+	0.727861i	$0.259486\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.49437	−	8.49437i	−0.393072	−	0.393072i	0.482709	−	0.875781i	$-0.339653\pi$
$467$	−8.49437	−	8.49437i	−0.393072	−	0.393072i	−0.875781	+	0.482709i	$0.839653\pi$
$468$		0			0
$469$	14.6460			0.676290
$470$		0			0
$471$			46.1725i			2.12752i
$472$		0			0
$473$	3.11871	−	3.11871i	0.143399	−	0.143399i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−63.8999	+	63.8999i	−2.92578	+	2.92578i
$478$		0			0
$479$		−	15.9307i		−	0.727890i	−0.931420	−	0.363945i	$-0.881430\pi$
$479$		−	15.9307i		−	0.727890i	0.931420	−	0.363945i	$-0.118570\pi$
$480$		0			0
$481$	−4.62927			−0.211077
$482$		0			0
$483$	−12.4773	−	12.4773i	−0.567736	−	0.567736i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	1.02714	−	1.02714i	0.0465441	−	0.0465441i	−0.683452	−	0.729996i	$-0.739522\pi$
$487$	1.02714	−	1.02714i	0.0465441	−	0.0465441i	0.729996	+	0.683452i	$0.239522\pi$
$488$		0			0
$489$	46.9321			2.12234
$490$		0			0
$491$	−16.1866			−0.730493			−0.365246	−	0.930911i	$-0.619015\pi$
$491$	−16.1866			−0.730493			−0.365246	+	0.930911i	$0.619015\pi$
$492$		0			0
$493$	−14.2254	−	14.2254i	−0.640681	−	0.640681i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.50696	−	4.50696i	0.202165	−	0.202165i
$498$		0			0
$499$			15.0943i			0.675713i	0.941198	+	0.337856i	$0.109702\pi$
$499$			15.0943i			0.675713i	−0.941198	+	0.337856i	$0.890298\pi$
$500$		0			0
$501$	−19.9307			−0.890436
$502$		0			0
$503$	26.9429	−	26.9429i	1.20132	−	1.20132i	0.227559	−	0.973764i	$-0.426925\pi$
$503$	26.9429	−	26.9429i	1.20132	−	1.20132i	0.973764	−	0.227559i	$-0.0730745\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	28.4344	−	28.4344i	1.26282	−	1.26282i
$508$		0			0
$509$	−24.6484			−1.09252			−0.546261	−	0.837615i	$-0.683949\pi$
$509$	−24.6484			−1.09252			−0.546261	+	0.837615i	$0.683949\pi$
$510$		0			0
$511$	18.3488			0.811705
$512$		0			0
$513$	−20.0993	−	54.1256i	−0.887406	−	2.38971i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−5.50659	−	5.50659i	−0.242179	−	0.242179i
$518$		0			0
$519$		−	18.3430i		−	0.805167i
$520$		0			0
$521$		−	7.60481i		−	0.333173i	−0.986027	−	0.166586i	$-0.946726\pi$
$521$		−	7.60481i		−	0.333173i	0.986027	−	0.166586i	$-0.0532745\pi$
$522$		0			0
$523$	−22.5645	−	22.5645i	−0.986675	−	0.986675i	0.0132372	−	0.999912i	$-0.495786\pi$
$523$	−22.5645	−	22.5645i	−0.986675	−	0.986675i	−0.999912	+	0.0132372i	$0.995786\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.0706	−	21.0706i	0.917850	−	0.917850i
$528$		0			0
$529$			16.0132i			0.696225i
$530$		0			0
$531$		−	92.5367i		−	4.01575i
$532$		0			0
$533$	4.88717	−	4.88717i	0.211687	−	0.211687i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.47486	+	6.47486i	0.279411	+	0.279411i
$538$		0			0
$539$		−	2.10554i		−	0.0906920i
$540$		0			0
$541$	36.3331			1.56208			0.781041	−	0.624479i	$-0.214689\pi$
$541$	36.3331			1.56208			0.781041	+	0.624479i	$0.214689\pi$
$542$		0			0
$543$	−40.6253	+	40.6253i	−1.74340	+	1.74340i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.18103	−	7.18103i	0.307039	−	0.307039i	−0.536721	−	0.843760i	$-0.680337\pi$
$547$	7.18103	−	7.18103i	0.307039	−	0.307039i	0.843760	+	0.536721i	$0.180337\pi$
$548$		0			0
$549$		−	15.4314i		−	0.658595i
$550$		0			0
$551$	−8.18664	+	17.8583i	−0.348763	+	0.760790i
$552$		0			0
$553$	2.16872	+	2.16872i	0.0922234	+	0.0922234i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−24.3054	−	24.3054i	−1.02985	−	1.02985i	−0.999541	−	0.0303105i	$-0.990350\pi$
$557$	−24.3054	−	24.3054i	−1.02985	−	1.02985i	−0.0303105	−	0.999541i	$-0.509650\pi$
$558$		0			0
$559$	−3.38181			−0.143035
$560$		0			0
$561$		−	11.4666i		−	0.484120i
$562$		0			0
$563$	−15.7743	−	15.7743i	−0.664809	−	0.664809i	0.291700	−	0.956510i	$-0.405779\pi$
$563$	−15.7743	−	15.7743i	−0.664809	−	0.664809i	−0.956510	+	0.291700i	$0.905779\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−30.7259	−	30.7259i	−1.29037	−	1.29037i
$568$		0			0
$569$	4.45189			0.186633			0.0933164	−	0.995637i	$-0.470253\pi$
$569$	4.45189			0.186633			0.0933164	+	0.995637i	$0.470253\pi$
$570$		0			0
$571$	29.6834			1.24221			0.621105	−	0.783727i	$-0.286684\pi$
$571$	29.6834			1.24221			0.621105	+	0.783727i	$0.286684\pi$
$572$		0			0
$573$	−10.0024	−	10.0024i	−0.417857	−	0.417857i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.7235	+	12.7235i	0.529688	+	0.529688i	0.920479	−	0.390791i	$-0.127799\pi$
$577$	12.7235	+	12.7235i	0.529688	+	0.529688i	−0.390791	+	0.920479i	$0.627799\pi$
$578$		0			0
$579$		−	19.9307i		−	0.828290i
$580$		0			0
$581$	−15.7743			−0.654430
$582$		0			0
$583$	7.19747	+	7.19747i	0.298089	+	0.298089i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.48849	−	2.48849i	−0.102711	−	0.102711i	0.653884	−	0.756595i	$-0.273138\pi$
$587$	−2.48849	−	2.48849i	−0.102711	−	0.102711i	−0.756595	+	0.653884i	$0.773138\pi$
$588$		0			0
$589$	−26.4516	−	12.1260i	−1.08992	−	0.499643i
$590$		0			0
$591$		−	46.7848i		−	1.92447i
$592$		0			0
$593$	2.78892	−	2.78892i	0.114527	−	0.114527i	−0.647521	−	0.762048i	$-0.724194\pi$
$593$	2.78892	−	2.78892i	0.114527	−	0.114527i	0.762048	+	0.647521i	$0.224194\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	18.5629	−	18.5629i	0.759727	−	0.759727i
$598$		0			0
$599$	46.1947			1.88746			0.943732	−	0.330711i	$-0.107288\pi$
$599$	46.1947			1.88746			0.943732	+	0.330711i	$0.107288\pi$
$600$		0			0
$601$		−	28.8714i		−	1.17769i	−0.808246	−	0.588845i	$-0.799583\pi$
$601$		−	28.8714i		−	1.17769i	0.808246	−	0.588845i	$-0.200417\pi$
$602$		0			0
$603$	35.3808	+	35.3808i	1.44082	+	1.44082i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−15.5365	+	15.5365i	−0.630608	+	0.630608i	−0.948220	−	0.317613i	$-0.897119\pi$
$607$	−15.5365	+	15.5365i	−0.630608	+	0.630608i	0.317613	+	0.948220i	$0.397119\pi$
$608$		0			0
$609$			30.0870i			1.21919i
$610$		0			0
$611$			5.97113i			0.241566i
$612$		0			0
$613$	−23.4241	+	23.4241i	−0.946089	+	0.946089i	−0.998619	−	0.0525301i	$-0.983271\pi$
$613$	−23.4241	+	23.4241i	−0.946089	+	0.946089i	0.0525301	+	0.998619i	$0.483271\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.4558	+	16.4558i	0.662486	+	0.662486i	0.955965	−	0.293480i	$-0.0948133\pi$
$617$	16.4558	+	16.4558i	0.662486	+	0.662486i	−0.293480	+	0.955965i	$0.594813\pi$
$618$		0			0
$619$			41.2711i			1.65882i	0.558637	+	0.829412i	$0.311324\pi$
$619$			41.2711i			1.65882i	−0.558637	+	0.829412i	$0.688676\pi$
$620$		0			0
$621$		−	35.0121i		−	1.40499i
$622$		0			0
$623$	21.0706	+	21.0706i	0.844176	+	0.844176i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−10.4969	+	3.89799i	−0.419207	+	0.155671i
$628$		0			0
$629$	−33.4335			−1.33308
$630$		0			0
$631$	27.1939			1.08257			0.541287	−	0.840838i	$-0.317937\pi$
$631$	27.1939			1.08257			0.541287	+	0.840838i	$0.317937\pi$
$632$		0			0
$633$	50.7816	−	50.7816i	2.01839	−	2.01839i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.14158	+	1.14158i	−0.0452311	+	0.0452311i
$638$		0			0
$639$	21.7752			0.861412
$640$		0			0
$641$			4.96042i			0.195925i	0.995190	+	0.0979625i	$0.0312325\pi$
$641$			4.96042i			0.195925i	−0.995190	+	0.0979625i	$0.968767\pi$
$642$		0			0
$643$	−20.3176	+	20.3176i	−0.801247	+	0.801247i	−0.983290	−	0.182044i	$-0.941729\pi$
$643$	−20.3176	+	20.3176i	−0.801247	+	0.801247i	0.182044	+	0.983290i	$0.441729\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.16125	−	8.16125i	−0.320852	−	0.320852i	0.528242	−	0.849094i	$-0.322851\pi$
$647$	−8.16125	−	8.16125i	−0.320852	−	0.320852i	−0.849094	+	0.528242i	$0.822851\pi$
$648$		0			0
$649$	−10.4230			−0.409139
$650$		0			0
$651$	−44.5647			−1.74663
$652$		0			0
$653$	23.4387	−	23.4387i	0.917226	−	0.917226i	−0.0796012	−	0.996827i	$-0.525365\pi$
$653$	23.4387	−	23.4387i	0.917226	−	0.917226i	0.996827	+	0.0796012i	$0.0253647\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	44.3258	+	44.3258i	1.72932	+	1.72932i
$658$		0			0
$659$	−6.84519			−0.266651			−0.133325	−	0.991072i	$-0.542566\pi$
$659$	−6.84519			−0.266651			−0.133325	+	0.991072i	$0.542566\pi$
$660$		0			0
$661$			13.0674i			0.508263i	0.967170	+	0.254131i	$0.0817896\pi$
$661$			13.0674i			0.508263i	−0.967170	+	0.254131i	$0.918210\pi$
$662$		0			0
$663$	−6.21696	+	6.21696i	−0.241447	+	0.241447i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.42380	+	8.42380i	−0.326171	+	0.326171i
$668$		0			0
$669$			60.5560i			2.34123i
$670$		0			0
$671$	−1.73813			−0.0671000
$672$		0			0
$673$	−9.16699	−	9.16699i	−0.353361	−	0.353361i	0.507997	−	0.861359i	$-0.330386\pi$
$673$	−9.16699	−	9.16699i	−0.353361	−	0.353361i	−0.861359	+	0.507997i	$0.830386\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.13824	+	4.13824i	−0.159046	+	0.159046i	−0.782144	−	0.623098i	$-0.785874\pi$
$677$	−4.13824	+	4.13824i	−0.159046	+	0.159046i	0.623098	+	0.782144i	$0.285874\pi$
$678$		0			0
$679$	22.1142			0.848665
$680$		0			0
$681$	−18.3430			−0.702904
$682$		0			0
$683$	−34.7907	−	34.7907i	−1.33123	−	1.33123i	−0.904273	−	0.426956i	$-0.859586\pi$
$683$	−34.7907	−	34.7907i	−1.33123	−	1.33123i	−0.426956	−	0.904273i	$-0.640414\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−10.0707	+	10.0707i	−0.384223	+	0.384223i
$688$		0			0
$689$		−	7.80465i		−	0.297333i
$690$		0			0
$691$	11.1939			0.425837			0.212919	−	0.977070i	$-0.431703\pi$
$691$	11.1939			0.425837			0.212919	+	0.977070i	$0.431703\pi$
$692$		0			0
$693$	−8.54420	+	8.54420i	−0.324567	+	0.324567i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	35.2960	−	35.2960i	1.33693	−	1.33693i
$698$		0			0
$699$	50.0787			1.89415
$700$		0			0
$701$	−1.75386			−0.0662425			−0.0331213	−	0.999451i	$-0.510545\pi$
$701$	−1.75386			−0.0662425			−0.0331213	+	0.999451i	$0.510545\pi$
$702$		0			0
$703$	11.3655	+	30.6062i	0.428657	+	1.15434i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.04491	+	6.04491i	0.227342	+	0.227342i
$708$		0			0
$709$		−	27.4109i		−	1.02944i	−0.857359	−	0.514719i	$-0.827896\pi$
$709$		−	27.4109i		−	1.02944i	0.857359	−	0.514719i	$-0.172104\pi$
$710$		0			0
$711$			10.4781i			0.392959i
$712$		0			0
$713$	−12.4773	−	12.4773i	−0.467278	−	0.467278i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	23.5233	−	23.5233i	0.878493	−	0.878493i
$718$		0			0
$719$			18.2170i			0.679378i	0.940538	+	0.339689i	$0.110322\pi$
$719$			18.2170i			0.679378i	−0.940538	+	0.339689i	$0.889678\pi$
$720$		0			0
$721$		−	3.88397i		−	0.144647i
$722$		0			0
$723$	−30.7269	+	30.7269i	−1.14274	+	1.14274i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−2.28726	−	2.28726i	−0.0848297	−	0.0848297i	0.663419	−	0.748248i	$-0.269105\pi$
$727$	−2.28726	−	2.28726i	−0.0848297	−	0.0848297i	−0.748248	+	0.663419i	$0.769105\pi$
$728$		0			0
$729$		−	21.8119i		−	0.807850i
$730$		0			0
$731$	−24.4241			−0.903357
$732$		0			0
$733$	−25.8872	+	25.8872i	−0.956164	+	0.956164i	−0.999079	−	0.0429145i	$-0.986336\pi$
$733$	−25.8872	+	25.8872i	−0.956164	+	0.956164i	0.0429145	+	0.999079i	$0.486336\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.98517	−	3.98517i	0.146796	−	0.146796i
$738$		0			0
$739$		−	48.8021i		−	1.79521i	−0.440797	−	0.897607i	$-0.645304\pi$
$739$		−	48.8021i		−	1.79521i	0.440797	−	0.897607i	$-0.354696\pi$
$740$		0			0
$741$	7.80465	+	3.57782i	0.286711	+	0.131435i
$742$		0			0
$743$	−0.674864	−	0.674864i	−0.0247583	−	0.0247583i	0.694619	−	0.719378i	$-0.255573\pi$
$743$	−0.674864	−	0.674864i	−0.0247583	−	0.0247583i	−0.719378	+	0.694619i	$0.755573\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−38.1065	−	38.1065i	−1.39424	−	1.39424i
$748$		0			0
$749$	21.0706			0.769903
$750$		0			0
$751$			11.7727i			0.429593i	0.976659	+	0.214797i	$0.0689089\pi$
$751$			11.7727i			0.429593i	−0.976659	+	0.214797i	$0.931091\pi$
$752$		0			0
$753$	20.1965	+	20.1965i	0.736003	+	0.736003i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−36.0943	−	36.0943i	−1.31187	−	1.31187i	−0.920037	−	0.391832i	$-0.871841\pi$
$757$	−36.0943	−	36.0943i	−1.31187	−	1.31187i	−0.391832	−	0.920037i	$-0.628159\pi$
$758$		0			0
$759$	−6.79012			−0.246466
$760$		0			0
$761$	−18.6194			−0.674953			−0.337477	−	0.941334i	$-0.609573\pi$
$761$	−18.6194			−0.674953			−0.337477	+	0.941334i	$0.609573\pi$
$762$		0			0
$763$	28.6203	+	28.6203i	1.03613	+	1.03613i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.65115	+	5.65115i	0.204051	+	0.204051i
$768$		0			0
$769$		−	23.5720i		−	0.850027i	−0.905187	−	0.425013i	$-0.860269\pi$
$769$		−	23.5720i		−	0.850027i	0.905187	−	0.425013i	$-0.139731\pi$
$770$		0			0
$771$	30.4690			1.09731
$772$		0			0
$773$	−27.7627	−	27.7627i	−0.998556	−	0.998556i	0.00144323	−	0.999999i	$-0.499541\pi$
$773$	−27.7627	−	27.7627i	−0.998556	−	0.998556i	−0.999999	+	0.00144323i	$0.999541\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	35.3561	+	35.3561i	1.26839	+	1.26839i
$778$		0			0
$779$	−44.3099	−	20.3127i	−1.58757	−	0.727776i
$780$		0			0
$781$		−	2.45268i		−	0.0877637i
$782$		0			0
$783$	−42.2130	+	42.2130i	−1.50857	+	1.50857i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−20.7019	+	20.7019i	−0.737943	+	0.737943i	−0.972180	−	0.234237i	$-0.924741\pi$
$787$	−20.7019	+	20.7019i	−0.737943	+	0.737943i	0.234237	+	0.972180i	$0.424741\pi$
$788$		0			0
$789$	19.6615			0.699968
$790$		0			0
$791$		−	18.4813i		−	0.657119i
$792$		0			0
$793$	0.942383	+	0.942383i	0.0334650	+	0.0334650i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.81471	+	8.81471i	−0.312233	+	0.312233i	−0.845774	−	0.533541i	$-0.820861\pi$
$797$	−8.81471	+	8.81471i	−0.312233	+	0.312233i	0.533541	+	0.845774i	$0.320861\pi$
$798$		0			0
$799$			43.1246i			1.52564i
$800$		0			0
$801$			101.802i			3.59699i
$802$		0			0
$803$	4.99271	−	4.99271i	0.176189	−	0.176189i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	39.2955	+	39.2955i	1.38327	+	1.38327i
$808$		0			0
$809$		−	6.73672i		−	0.236850i	−0.992963	−	0.118425i	$-0.962215\pi$
$809$		−	6.73672i		−	0.236850i	0.992963	−	0.118425i	$-0.0377846\pi$
$810$		0			0
$811$		−	1.29466i		−	0.0454616i	−0.999742	−	0.0227308i	$-0.992764\pi$
$811$		−	1.29466i		−	0.0454616i	0.999742	−	0.0227308i	$-0.00723606\pi$
$812$		0			0
$813$	−18.6641	−	18.6641i	−0.654577	−	0.654577i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	8.30280	+	22.3587i	0.290478	+	0.782232i
$818$		0			0
$819$	9.26499			0.323745
$820$		0			0
$821$	−23.7137			−0.827614			−0.413807	−	0.910365i	$-0.635801\pi$
$821$	−23.7137			−0.827614			−0.413807	+	0.910365i	$0.635801\pi$
$822$		0			0
$823$	−2.15140	+	2.15140i	−0.0749931	+	0.0749931i	−0.743608	−	0.668615i	$-0.766887\pi$
$823$	−2.15140	+	2.15140i	−0.0749931	+	0.0749931i	0.668615	+	0.743608i	$0.266887\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−17.4896	+	17.4896i	−0.608173	+	0.608173i	−0.942468	−	0.334295i	$-0.891502\pi$
$827$	−17.4896	+	17.4896i	−0.608173	+	0.608173i	0.334295	+	0.942468i	$0.391502\pi$
$828$		0			0
$829$	−21.7752			−0.756283			−0.378141	−	0.925748i	$-0.623437\pi$
$829$	−21.7752			−0.756283			−0.378141	+	0.925748i	$0.623437\pi$
$830$		0			0
$831$			44.1955i			1.53312i
$832$		0			0
$833$	−8.24472	+	8.24472i	−0.285663	+	0.285663i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−62.5256	−	62.5256i	−2.16120	−	2.16120i
$838$		0			0
$839$	−30.6196			−1.05710			−0.528552	−	0.848901i	$-0.677265\pi$
$839$	−30.6196			−1.05710			−0.528552	+	0.848901i	$0.677265\pi$
$840$		0			0
$841$	−8.68735			−0.299564
$842$		0			0
$843$	12.7659	−	12.7659i	0.439681	−	0.439681i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−15.3307	−	15.3307i	−0.526771	−	0.526771i
$848$		0			0
$849$	−18.8468			−0.646821
$850$		0			0
$851$			19.7981i			0.678672i
$852$		0			0
$853$	7.18664	−	7.18664i	0.246066	−	0.246066i	−0.573288	−	0.819354i	$-0.694332\pi$
$853$	7.18664	−	7.18664i	0.246066	−	0.246066i	0.819354	+	0.573288i	$0.194332\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	19.3522	−	19.3522i	0.661057	−	0.661057i	−0.294572	−	0.955629i	$-0.595177\pi$
$857$	19.3522	−	19.3522i	0.661057	−	0.661057i	0.955629	+	0.294572i	$0.0951770\pi$
$858$		0			0
$859$			30.5599i			1.04269i	0.853346	+	0.521346i	$0.174570\pi$
$859$			30.5599i			1.04269i	−0.853346	+	0.521346i	$0.825430\pi$
$860$		0			0
$861$	−74.6516			−2.54412
$862$		0			0
$863$	−0.199200	−	0.199200i	−0.00678084	−	0.00678084i	0.703708	−	0.710489i	$-0.251526\pi$
$863$	−0.199200	−	0.199200i	−0.00678084	−	0.00678084i	−0.710489	+	0.703708i	$0.751526\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.59092	+	6.59092i	−0.223839	+	0.223839i
$868$		0			0
$869$	1.18021			0.0400360
$870$		0			0
$871$	−4.32136			−0.146424
$872$		0			0
$873$	53.4219	+	53.4219i	1.80806	+	1.80806i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.1546	+	23.1546i	−0.781874	+	0.781874i	−0.980147	−	0.198273i	$-0.936467\pi$
$877$	−23.1546	+	23.1546i	−0.781874	+	0.781874i	0.198273	+	0.980147i	$0.436467\pi$
$878$		0			0
$879$		−	33.1286i		−	1.11740i
$880$		0			0
$881$	9.84367			0.331642			0.165821	−	0.986156i	$-0.446973\pi$
$881$	9.84367			0.331642			0.165821	+	0.986156i	$0.446973\pi$
$882$		0			0
$883$	−3.71274	+	3.71274i	−0.124944	+	0.124944i	−0.766814	−	0.641870i	$-0.778159\pi$
$883$	−3.71274	+	3.71274i	−0.124944	+	0.124944i	0.641870	+	0.766814i	$0.278159\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−35.8697	+	35.8697i	−1.20439	+	1.20439i	−0.231568	+	0.972819i	$0.574385\pi$
$887$	−35.8697	+	35.8697i	−1.20439	+	1.20439i	−0.972819	+	0.231568i	$0.925615\pi$
$888$		0			0
$889$	−29.0409			−0.974002
$890$		0			0
$891$	−16.7210			−0.560174
$892$		0			0
$893$	39.4779	−	14.6599i	1.32108	−	0.490575i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	3.68147	+	3.68147i	0.122921	+	0.122921i
$898$		0			0
$899$			30.0870i			1.00346i
$900$		0			0
$901$		−	56.3666i		−	1.87784i
$902$		0			0
$903$	25.8286	+	25.8286i	0.859523	+	0.859523i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−6.52260	+	6.52260i	−0.216579	+	0.216579i	−0.807055	−	0.590476i	$-0.798940\pi$
$907$	−6.52260	+	6.52260i	−0.216579	+	0.216579i	0.590476	+	0.807055i	$0.298940\pi$
$908$		0			0
$909$			29.2057i			0.968692i
$910$		0			0
$911$			20.4476i			0.677460i	0.940884	+	0.338730i	$0.109997\pi$
$911$			20.4476i			0.677460i	−0.940884	+	0.338730i	$0.890003\pi$
$912$		0			0
$913$	−4.29218	+	4.29218i	−0.142051	+	0.142051i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.5515	−	13.5515i	−0.447510	−	0.447510i
$918$		0			0
$919$		−	13.9756i		−	0.461011i	−0.973071	−	0.230506i	$-0.925962\pi$
$919$		−	13.9756i		−	0.461011i	0.973071	−	0.230506i	$-0.0740380\pi$
$920$		0			0
$921$	105.429			3.47399
$922$		0			0
$923$	−1.32979	+	1.32979i	−0.0437707	+	0.0437707i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	9.38262	−	9.38262i	0.308166	−	0.308166i
$928$		0			0
$929$			22.9478i			0.752893i	0.926438	+	0.376446i	$0.122854\pi$
$929$			22.9478i			0.752893i	−0.926438	+	0.376446i	$0.877146\pi$
$930$		0			0
$931$	10.3503	+	4.74479i	0.339216	+	0.155504i
$932$		0			0
$933$	25.3619	+	25.3619i	0.830312	+	0.830312i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.9076	+	11.9076i	0.389005	+	0.389005i	0.874333	−	0.485327i	$-0.161300\pi$
$937$	11.9076	+	11.9076i	0.389005	+	0.389005i	−0.485327	+	0.874333i	$0.661300\pi$
$938$		0			0
$939$	−65.5172			−2.13807
$940$		0			0
$941$			34.1709i			1.11394i	0.830533	+	0.556969i	$0.188036\pi$
$941$			34.1709i			1.11394i	−0.830533	+	0.556969i	$0.811964\pi$
$942$		0			0
$943$	−20.9011	−	20.9011i	−0.680633	−	0.680633i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.00096	+	6.00096i	0.195005	+	0.195005i	0.797855	−	0.602850i	$-0.205968\pi$
$947$	6.00096	+	6.00096i	0.195005	+	0.195005i	−0.602850	+	0.797855i	$0.705968\pi$
$948$		0			0
$949$	−5.41389			−0.175742
$950$		0			0
$951$	−44.4906			−1.44271
$952$		0			0
$953$	16.0583	+	16.0583i	0.520179	+	0.520179i	0.917626	−	0.397446i	$-0.130103\pi$
$953$	16.0583	+	16.0583i	0.520179	+	0.520179i	−0.397446	+	0.917626i	$0.630103\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	8.18664	+	8.18664i	0.264637	+	0.264637i
$958$		0			0
$959$		−	9.44007i		−	0.304836i
$960$		0			0
$961$	−13.5647			−0.437570
$962$		0			0
$963$	50.9009	+	50.9009i	1.64026	+	1.64026i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−16.6956	−	16.6956i	−0.536894	−	0.536894i	0.385721	−	0.922615i	$-0.373953\pi$
$967$	−16.6956	−	16.6956i	−0.536894	−	0.536894i	−0.922615	+	0.385721i	$0.873953\pi$
$968$		0			0
$969$	56.3666	+	25.8397i	1.81076	+	0.830091i
$970$		0			0
$971$		−	10.6476i		−	0.341698i	−0.985297	−	0.170849i	$-0.945349\pi$
$971$		−	10.6476i		−	0.341698i	0.985297	−	0.170849i	$-0.0546510\pi$
$972$		0			0
$973$	−22.5804	+	22.5804i	−0.723894	+	0.723894i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.3085	+	29.3085i	−0.937661	+	0.937661i	−0.998168	−	0.0605070i	$-0.980728\pi$
$977$	−29.3085	+	29.3085i	−0.937661	+	0.937661i	0.0605070	+	0.998168i	$0.480728\pi$
$978$		0			0
$979$	11.4666			0.366474
$980$		0			0
$981$			138.278i			4.41488i
$982$		0			0
$983$	−2.77527	−	2.77527i	−0.0885172	−	0.0885172i	0.661462	−	0.749979i	$-0.269936\pi$
$983$	−2.77527	−	2.77527i	−0.0885172	−	0.0885172i	−0.749979	+	0.661462i	$0.769936\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	45.6046	−	45.6046i	1.45161	−	1.45161i
$988$		0			0
$989$			14.4631i			0.459900i
$990$		0			0
$991$		−	9.18342i		−	0.291721i	−0.989305	−	0.145861i	$-0.953405\pi$
$991$		−	9.18342i		−	0.291721i	0.989305	−	0.145861i	$-0.0465951\pi$
$992$		0			0
$993$	−45.7704	+	45.7704i	−1.45248	+	1.45248i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	37.8773	+	37.8773i	1.19959	+	1.19959i	0.974290	+	0.225296i	$0.0723350\pi$
$997$	37.8773	+	37.8773i	1.19959	+	1.19959i	0.225296	+	0.974290i	$0.427665\pi$
$998$		0			0
$999$			99.2116i			3.13892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.l.b.1557.6		12
5.2	odd	4		380.2.l.b.113.6	yes	12
5.3	odd	4	inner	1900.2.l.b.493.1		12
5.4	even	2		380.2.l.b.37.1	✓	12
15.2	even	4		3420.2.bb.d.2773.5		12
15.14	odd	2		3420.2.bb.d.37.6		12
19.18	odd	2	inner	1900.2.l.b.1557.1		12
95.18	even	4	inner	1900.2.l.b.493.6		12
95.37	even	4		380.2.l.b.113.1	yes	12
95.94	odd	2		380.2.l.b.37.6	yes	12
285.227	odd	4		3420.2.bb.d.2773.6		12
285.284	even	2		3420.2.bb.d.37.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.l.b.37.1	✓	12	5.4	even	2
380.2.l.b.37.6	yes	12	95.94	odd	2
380.2.l.b.113.1	yes	12	95.37	even	4
380.2.l.b.113.6	yes	12	5.2	odd	4
1900.2.l.b.493.1		12	5.3	odd	4	inner
1900.2.l.b.493.6		12	95.18	even	4	inner
1900.2.l.b.1557.1		12	19.18	odd	2	inner
1900.2.l.b.1557.6		12	1.1	even	1	trivial
3420.2.bb.d.37.5		12	285.284	even	2
3420.2.bb.d.37.6		12	15.14	odd	2
3420.2.bb.d.2773.5		12	15.2	even	4
3420.2.bb.d.2773.6		12	285.227	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.25348 + 2.25348i) q^{3} +(1.48119 + 1.48119i) q^{7} +7.15633i q^{9} +O(q^{10})\)	\(q+(2.25348 + 2.25348i) q^{3} +(1.48119 + 1.48119i) q^{7} +7.15633i q^{9} +0.806063 q^{11} +(-0.437032 - 0.437032i) q^{13} +(-3.15633 - 3.15633i) q^{17} +(-1.81645 + 3.96239i) q^{19} +6.67568i q^{21} +(-1.86907 + 1.86907i) q^{23} +(-9.36619 + 9.36619i) q^{27} +4.50696 q^{29} +6.67568i q^{31} +(1.81645 + 1.81645i) q^{33} +(5.29626 - 5.29626i) q^{37} -1.96968i q^{39} +11.1826i q^{41} +(3.86907 - 3.86907i) q^{43} +(-6.83146 - 6.83146i) q^{47} -2.61213i q^{49} -14.2254i q^{51} +(8.92916 + 8.92916i) q^{53} +(-13.0225 + 4.83583i) q^{57} -12.9308 q^{59} -2.15633 q^{61} +(-10.5999 + 10.5999i) q^{63} +(4.94399 - 4.94399i) q^{67} -8.42380 q^{69} -3.04278i q^{71} +(6.19394 - 6.19394i) q^{73} +(1.19394 + 1.19394i) q^{77} +1.46417 q^{79} -20.7440 q^{81} +(-5.32487 + 5.32487i) q^{83} +(10.1563 + 10.1563i) q^{87} +14.2254 q^{89} -1.29466i q^{91} +(-15.0435 + 15.0435i) q^{93} +(7.46498 - 7.46498i) q^{97} +5.76845i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{7}+O(q^{10}) \) 12 * q - 4 * q^7	\( 12 q - 4 q^{7} + 8 q^{11} + 4 q^{17} - 4 q^{23} + 28 q^{43} - 20 q^{47} - 24 q^{57} + 16 q^{61} - 20 q^{63} + 76 q^{73} + 16 q^{77} + 4 q^{81} - 84 q^{83} + 80 q^{87} - 8 q^{93}+O(q^{100}) \) 12 * q - 4 * q^7 + 8 * q^11 + 4 * q^17 - 4 * q^23 + 28 * q^43 - 20 * q^47 - 24 * q^57 + 16 * q^61 - 20 * q^63 + 76 * q^73 + 16 * q^77 + 4 * q^81 - 84 * q^83 + 80 * q^87 - 8 * q^93

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